Military exercises involve the USS John C Stennis and the USS Dwight D Eisenhower, marking the first time that the two strike groups have operated in a joint exercise under the Fifth Fleet, the navy said.
"Two air wings from the aircraft carriers will conduct air warfare exercises while the surface components will conduct exercises in three general disciplines: anti-submarine, anti-surface and mine warfare," it said.
The Fifth Fleet is based in Bahrain, an island state that lies across the Gulf from Iran.
The US exercises come after Iran's capture last week of 15 British sailors and marines who Tehran claims had strayed into Iranian waters near the Gulf.
Britain and the US navy have insisted the British sailors were operating in Iraqi waters.
Aandahl said the US manoeuvres were not meant to threaten the Islamic Republic, whose navy operates in the same waters.
Aandahl said the US warships would stay out of Iranian territorial waters, which extend 12 miles off the Iranian coast.
A French naval strike group, led by the aircraft carrier Charles de Gaulle, is operating simultaneously just outside the Gulf.
But the French ships are supporting the Nato forces in Afghanistan and not taking part in the American manoeuvres, officials said.
Overall, the exercises involve more than 10,000 US personnel on warships and aircraft making simulated attacks on enemy shipping with aircraft and ships, hunting enemy submarines and finding mines.